6533b853fe1ef96bd12ad5eb

RESEARCH PRODUCT

Ledrappier-Young formula and exact dimensionality of self-affine measures

Antti KäenmäkiAntti KäenmäkiBalázs BárányBalázs Bárány

subject

local dimensionPlane (geometry)General MathematicsOpen problem010102 general mathematicsMathematical analysista111Dynamical Systems (math.DS)01 natural sciencesMeasure (mathematics)self-affine set010101 applied mathematicsIterated function systemself-affine measureHausdorff dimension37C45 28A80FOS: MathematicsApplied mathematicsAffine transformation0101 mathematicsMathematics - Dynamical Systemshausdorff dimensionMathematicsCurse of dimensionality

description

In this paper, we solve the long standing open problem on exact dimensionality of self-affine measures on the plane. We show that every self-affine measure on the plane is exact dimensional regardless of the choice of the defining iterated function system. In higher dimensions, under certain assumptions, we prove that self-affine and quasi self-affine measures are exact dimensional. In both cases, the measures satisfy the Ledrappier-Young formula. peerReviewed

yearjournalcountryeditionlanguage
2017-01-01
10.1016/j.aim.2017.07.015http://arxiv.org/abs/1511.05792